Numerical simulation of the Riesz fractional diffusion equation with a nonlinear source term
Data(s) |
2008
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Resumo |
In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and Gr¨unwald-Letnikov(GL) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis. |
Formato |
application/pdf |
Identificador | |
Publicador |
Springer |
Relação |
http://eprints.qut.edu.au/30897/1/Numerical_simulation_of_the_Riesz_fractional_diffusion_equation_with_a_nonlinear_source_term.pdf Zhang, Hong-Mei & Liu, Fawang (2008) Numerical simulation of the Riesz fractional diffusion equation with a nonlinear source term. Journal of Applied Mathematics and Informatics, 26(1-2), pp. 1-14. |
Direitos |
Copyright 2008 Springer |
Fonte |
Faculty of Science and Technology |
Palavras-Chave | #010204 Dynamical Systems in Applications #010301 Numerical Analysis #Riesz Fractional Derivatives, Implicit Difference Approximation, Nonlinear Source, Stability, Convergence |
Tipo |
Journal Article |